In practice, users may communicate with the server through intermediate relays [1]}.
A `symmetric' version of this general problem is known as the combination network with end-user-caches as shown in Fig. REF :
a server with \({\mathsf {N}}\)  files is connected to \({\mathsf {H}}\)  relays (without caches), which in turns are connected to \({\mathsf {K}}= \binom{{\mathsf {H}}}{{\mathsf {r}}}\)  users equipped with caches of size \({\mathsf {M}}\)  files and where each user is connected to a different subset of the \({\mathsf {r}}\)  relays.
All links are assumed to be error-free and interference-free. The objective is to determine the optimal max-link load \({\mathsf {R}}^{\star }\) , defined as the smallest max-rate
(the maximum rate among all the links, proportional to the download time)
for the worst case demands.
Combination networks with end-user-caches were originally studied in [2]} where a cut-set outer bound leveraging [3]} and two achievable schemes were proposed.
An achievable scheme was proposed in [4]} for the case where \({\mathsf {r}}\)  divides \({\mathsf {H}}\) ; the idea was to split the combination network into \({\mathsf {H}}\)  shared-link broadcast networks, in each of which the scheme in [3]} is used. Combination networks with caches at both the relays and the end-users has recently been considered in [6]} where an MDS code is used in both placement delivery phase. However, when there is no cache at the relay side, the scheme achieves the same load as [4]} without the condition that \({\mathsf {r}}\)  divides \({\mathsf {H}}\) .
In general, the fundamental limits of combination networks with end-user-caches are not known.
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